Suppose I stand on an electronic weighing scale, and it reports my weight as 74.5 kilos.
Usually a lot of books would say that the last digit is uncertain, and that the uncertainty is 0.1kg, and that my 'true' weight is between 74.4 and 74.6 kilos. But that kinda bothers me, because how do we know? Isn't the uncertainty depend on the type of equipment used, or various other factors?
Is the 0.1 of a unit some kind of standard when designing digital equipment? And, by the way, how do these equipment actually report the data? And how would the equipment 'guess' the last digit? How would the equipment 'decide' what to report as the final digit?
If let's say my true weight is precisely 74.5200000...., and obviously the equipment can only detect the smallest increment of 0.1kg, then how would the weighing scale decide the last digit? It would make more sense to me if the scale reports 74.5, because the extra bit (0.020000...) wouldn't be detectable by the scale? But thinking this way, the scale would've reported 74.5 even if my true weight is something like 74.5600000.... (even though it is now closer to 75.6, but the machine can't tell because it still cannot detect the extra 0.06000.... bit)
Thus taking these considerations into consideration, I don't really get the rationale behind interpreting the data as 74.5 +- 0.1, because if the machine works the way I've just described, then wouldn't it be better to just say that the true value lies between 74.5 and 74.6? Unless, of course, the machine doesn't work that way at all, which once again begs the same question: how does the equipment work?